Following Bridgeland [1]}, the DT invariants for the quiver \((Q,W)\) 
are determined by a
scattering diagram \(\mathcal {D}_Q\)  defined in the affine space \({R}^3\)  spanned by King stability (also
known as Fayet-Iliopoulos) parameters \((\theta _1,\theta _2,\theta _3)\) . For any dimension vector
\(\gamma =(n_1,n_2,n_3)\in {Z}^3\) , the active
ray \(\mathcal {R}_o(\gamma )\)  is defined as the locus where
\(\bar{\Omega }_\theta (\gamma )\ne 0\)  inside the hyperplane
\(\lbrace \theta \in {R}^3: n_1\theta _1+n_2\theta _2+n_3\theta _3=0\rbrace \) ,
where \(\bar{\Omega }_\theta (\gamma )\)  is the rational DT invariant associated to the moduli space of \(\theta \) -semistable representations of \((Q,W)\)  with dimension vector \(\gamma \)  (in particular,
\(\mathcal {R}_o(\gamma )\)  is empty unless the \(n_i\) 's are all positive). In §REF , building on earlier arguments [2]}, [3]}, [4]},
we prove that
the only initial rays are those for \(\gamma \in \lbrace \gamma _1,\gamma _2,\gamma _3,k\delta \rbrace \)  with
\(\gamma _1=(1,0,0),\gamma _2=(0,1,0),\gamma _3=(0,0,1),\delta =(1,1,1), k\ge 1\) , with DT invariants
\(\Omega _\star (k\gamma _i)=\delta _{k=1} \ ,\quad \Omega _\star (k\delta )=-y^3-y-1/y\) 
